The Riemann Hypothesis

In this article I describe a proof of the fact that ZFC cannot decide whether a certain modified Turing machine, or computer (satisfying a certain condition) will ever halt successfully in finite time. The consequences of this fact in relation to the Riemann Hypothesis are presented.

[1]  M. Riesz.  Sur l’hypothèse de Riemann , 1916 .

[2]  Harold M. Edwards,et al.  Riemann's Zeta Function , 1974 .

[3]  Tien D. Kieu,et al.  On the existence of a new family of Diophantine equations for z , 2003, Fundam. Informaticae.

[4]  K. Ramachandra.  ON THE MEAN-VALUE AND OMEGA-THEOREMS FOR THE RIEMANN ZETA-FUNCTION , 1995 .

[5]  John Derbyshire,et al.  Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics , 2003 .

[6]  W. Gruyter,et al.  More than two fifths of the zeros of the Riemann zeta function are on the critical line. , 1989 .

[7]  Cristian S. Calude,et al.  Finite Versus Infinite: Contributions to an Eternal Dilemma , 2000 .

[8]  E. N..  An Introduction to the Theory of Functions of a Complex Variable , 1936, Nature.

[9]  Tien D. Kieu,et al.  On the existence of a new family of Diophantine equations for Omega , 2003, ArXiv.

[10]  J. Littlewood,et al.  Contributions to the theory of the riemann zeta-function and the theory of the distribution of primes , 1916 .

[11]  D. R. Heath-Brown,et al.  The Theory of the Riemann Zeta-Function , 1987 .

[12]  Ernesto Oscar Reyes,et al.  The Riemann zeta function , 2004 .

[13]  Cabiria Andreian Cazacu,et al.  Fundamental Domains of Gamma and Zeta Functions , 2009, Int. J. Math. Math. Sci..

[14]  D. Ghisa,et al.  Colour visualization of Blaschke product mappings , 2008, 0812.0415.

[15]  J.-P. Gram,et al.  Note sur les zéros de la fonction ζ(s) de Riemann , 1903 .

[16]  Robert Spira,et al.  Zeros of sections of the zeta function. II , 1966 .

[17]  Robert M. Solovay.  A Version of Ω for which ZFC Cannot Predict a Single Bit , 2000, Finite Versus Infinite.

[18]  Viktor Moros.  THE ZETA FUNCTION AND THE RIEMANN HYPOTHESIS , 2014 .

[19]  C. Haselgrove,et al.  A disproof of a conjecture of Pólya , 1958 .

[20]  Cristian S. Calude,et al.  A New Measure of the Difficulty of Problems , 2006, J. Multiple Valued Log. Soft Comput..

[21]  Dorin Ghisa,et al.  Global mapping properties of rational functions , 2010 .

[22]  Cristian S. Calude.  Series Chaitin Ω Numbers , Solovay Machines , and Incompleteness , 1999 .

[23]  Marcus du Sautoy,et al.  The Music of the Primes , 2003 .

[24]  F. V. Atkinson,et al.  The Riemann zeta-function , 1950 .